The lion population in a certain reserve drops by $5\%$ every year. Currently, the population's size is $200$. Write a function that gives the lion population size, $P(t)$, $t$ years from today. $P(t)=$
Dropping by $5\%$ each year means the population keeps $100\%-5\%=95\%$ of its size each year. So each year, the population size is multiplied by $95\%$, which is the same as a factor of $0.95$. If we start with the initial value, $200$ lions, and keep multiplying by $0.95$, this function gives us the size of the population $t$ years from now: $P(t)=200(0.95)^t$